The temperature dependence of partition are as follows: qtranslation ∝ T3/2 qvibration ∝ T⁰ qrotation ∝ T… · ABC26PH0365

Subject: Physical Chemistry · Chapter: Statistical Thermodynamics · Topic: Statistical Thermodynamics – General · Exam: GATE 2005-2021 · Marks: 2 · Difficulty: Medium

The temperature dependence of partition are as follows:
\[ \begin{array}{ll} \mathrm{q}_{\text{translation}} \propto \mathrm{T}^{3/2} & \mathrm{q}_{\text{vibration}} \propto \mathrm{T}^{0} \\ \mathrm{q}_{\text{rotation}} \propto \mathrm{T}\,(\text{linear molecule}) & \mathrm{q}_{\text{rotation}} \propto \mathrm{T}^{3/2}\,(\text{non-linear molecule}) \end{array} \]
According to the Conventional Transition State Theory (CTST), the temperature dependence of the Arrhenius pre-exponential factor for a reaction of the type given below is linear molecule + linear molecule $\rightleftharpoons$ non-liner linear transition state $\rightarrow$ products.
(a)$\mathrm{T}^{-1}$
(b)$\mathrm{T}^{0}$
(c)$\mathrm{T}^{1}$
(d)$\mathrm{T}^{2}$
Answer
Answer: A ✓ checked by 4AB · confidence high
Explanation
A ∝ (kT/h)·q‡/(q_A q_B). Translation gives T^(3/2)/T³ and rotation gives T^(3/2)/T² (non-linear TS over two linear reactants). Total T · T^(−3/2) · T^(−1/2) = T⁻¹ (a).

Study loop for Statistical Thermodynamics

1. Practise the PYQsPrevious-year questions, with answers

· Browse this chapter in the app